A Gyrometer (or gyroscope) is a device for measuring orientation along one or several axis. In our case, we want a gyrometer to measure the rotation of the robot on the vertical axis to determine its orientation wrt the playing field.
To do so, we will need a Yaw gyrometer. Pitch and Roll are not necessary if we plan to stay on a horizontal surface, but can be useful to determine whether the robot is on a plane or not (for instance, auto-shutdown if it is held in someone's hand).
Some interesting products: